Abstract

These methods introduced by Henri Poincaré (1892) in his “Méthodes Nouvelles de la Mécanique Céleste” (“New Methods of Celestial Mechanics”) and by Aleksandr Lyapunov (1892, 1907) in his “General Problem of Motion Stability ” are part of Asymptotic Theories (see supra Part II). Faced with the three-body problem, (Poincaré 1892, 51) considered the approximation of the solution to the equations for the motion by using series expansions according to the increasing potency of a parameter μ assumed sufficiently small.